A body of mass 2 kg is lying on a rough inclined plane of inclination 30°. Find the magnitude of the force applied if push is applied horizontally and not parallel and Coefficient o f static friction=0.2.Concept of Physics - 1 , HC VERMA , Chapter 6:Friction "
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Solution :
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From the free body Diagram :
g=10m/s2
m=2kg
θ=30°
μ=0.2
FROM
R-mgcosθ-Fsinθ=0
R=mg cos θ+F sin θ------------(1)
and mgsinθ +μR -F Cos θ=0
mgSinθ +μ(mgCosθ+F sin θ )-Fcosθ=0
mgsinθ+μmgcosθ +μFsinθ -Fcos θ=o
F=mgSinθ+μmgCosθ/(μSinθ -Cos θ)
=(2x10 x 1/2 +0.2 x 2x10 x√3/2)/0.2 x 1/2 - (√3/2)
=13.464/0.76
17.7N=17.5 N
*****************************************
From the free body Diagram :
g=10m/s2
m=2kg
θ=30°
μ=0.2
FROM
R-mgcosθ-Fsinθ=0
R=mg cos θ+F sin θ------------(1)
and mgsinθ +μR -F Cos θ=0
mgSinθ +μ(mgCosθ+F sin θ )-Fcosθ=0
mgsinθ+μmgcosθ +μFsinθ -Fcos θ=o
F=mgSinθ+μmgCosθ/(μSinθ -Cos θ)
=(2x10 x 1/2 +0.2 x 2x10 x√3/2)/0.2 x 1/2 - (√3/2)
=13.464/0.76
17.7N=17.5 N
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